CN112943484B - Experimental device for researching heat transfer influence of roughness on wall surface of spray pipe - Google Patents
Experimental device for researching heat transfer influence of roughness on wall surface of spray pipe Download PDFInfo
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- CN112943484B CN112943484B CN202110070144.4A CN202110070144A CN112943484B CN 112943484 B CN112943484 B CN 112943484B CN 202110070144 A CN202110070144 A CN 202110070144A CN 112943484 B CN112943484 B CN 112943484B
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F02—COMBUSTION ENGINES; HOT-GAS OR COMBUSTION-PRODUCT ENGINE PLANTS
- F02K—JET-PROPULSION PLANTS
- F02K9/00—Rocket-engine plants, i.e. plants carrying both fuel and oxidant therefor; Control thereof
- F02K9/96—Rocket-engine plants, i.e. plants carrying both fuel and oxidant therefor; Control thereof characterised by specially adapted arrangements for testing or measuring
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F02—COMBUSTION ENGINES; HOT-GAS OR COMBUSTION-PRODUCT ENGINE PLANTS
- F02K—JET-PROPULSION PLANTS
- F02K9/00—Rocket-engine plants, i.e. plants carrying both fuel and oxidant therefor; Control thereof
- F02K9/97—Rocket nozzles
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Abstract
The invention discloses an experimental device for researching heat transfer influence of roughness on the wall surface of a spray pipe, which comprises: a nozzle housing having an inlet and an outlet, the nozzle housing presenting a cylindrical shape expanding from the inlet to the outlet; the graphite temperature measuring piece is of a hollow cylinder structure arranged close to the inner wall of the outlet section, the graphite temperature measuring piece is uniformly divided into n graphite temperature measuring units along the outer wall surface of the graphite temperature measuring piece, and the roughness of the surface of each graphite temperature measuring unit, which is in contact with the fuel gas, is different; the baffle plate is arranged at the outlet end of the spray pipe shell and is used for positioning the graphite temperature measuring piece; the thermocouple comprises a plurality of thermocouples, a plurality of thermocouple groups and a plurality of thermocouple groups, wherein the thermocouples are arranged on an outlet section of the spray pipe shell, are specifically distributed on a plurality of sections with different expansion ratios, and are arranged on each section in a surrounding manner and have different arrangement depths; the thermocouples are used for measuring the change rate of the temperature inside the wall surface of the outlet section of the spray pipe shell along with the working time of the engine, and the method for measuring the wall surface heat transfer process under the conditions of the same fuel gas parameters and different roughness in the spray pipe is provided.
Description
Technical Field
The invention belongs to the technical field of space engines, and particularly relates to an experimental device for researching heat transfer effect of roughness on a spray pipe wall surface.
Background
The solid rocket engine is one of the main engine types of modern rockets, aerospace systems and missile weapons, is widely applied to the aerospace technical field, has the characteristics of simple structure, high reliability, convenient use and the like, but has an extremely complex working process, and a series of difficult problems are caused by interaction of combustion and flow. The traditional solid rocket engine nozzle is generally designed according to the corresponding expansion ratio of the flying height of the traditional solid rocket engine nozzle, so that the nozzle is expected to keep a fully expanded working state in the working process, and the energy carried by the engine is utilized to the maximum extent. With conventional nozzles, the expansion ratio is determined such that, under ideal conditions, a fully expanded operating state is achieved only at a specific altitude. In reality, the nozzle cannot work normally due to various factors, such as back pressure change caused by flight height change, and throat area enlargement caused by erosion and ablation of the nozzle throat.
The gas flow of the flow field in the solid rocket engine is a complex physical and chemical process coupled with multi-phase interaction, wherein the interaction of all components of the gas at high temperature and high pressure, the constant and specific heat of mixed gas and the like are continuously changed along with the temperature and the component concentration, and the force and heat coupling of particle phase and the gas and other factors are bound to cause certain difficulty for accurate prediction of the flow field in the engine. The state of the flow field inside the jet pipe of the solid rocket engine is changed violently due to the transonic flow converted from the thermal kinetic energy of the fuel gas. Therefore, the research on the internal flow of the solid rocket engine jet pipe has important scientific significance and engineering value for disclosing the flow mechanism of the flow field of the engine jet pipe, obtaining the change rule of the fuel gas components in the jet pipe and providing necessary technical support for the novel jet pipe.
The charring layer is a dense, loose and porous irregular structure formed on the surface of the thermal insulation material in the ablation process. The charred layer left by ablation of the heat insulating layer in the solid rocket motor has the functions of flame retardance and heat insulation. The pore structure with compact surface can generate certain influence on the flow of the fuel gas in the flow field of the engine. Therefore, the study on the rough wall surface flow with the pit structure has important practical significance for further understanding the surface flow rule of the carbonization layer of the solid rocket engine and designing the engine structure and the internal heat insulation layer material thereof.
The ablation of the charring layer is a process which dynamically changes along with the working time of the engine, so the surface roughness of the charring layer also continuously changes along with the lapse of the working time of the engine, the change of the roughness has more obvious influence on the flow and heat transfer of a boundary layer between gas and a wall surface in the supersonic flow of the jet pipe, meanwhile, the consistency of gas parameters in multiple experiments is difficult to ensure by the current research means, and the slight change of a plurality of parameters can bring uncertainty to the experimental result in the supersonic flow. Therefore, how to measure the heat transfer process of the wall surface under the conditions of different roughness in the spray pipe under the same gas parameter is an urgent problem to be solved.
Disclosure of Invention
The invention aims to provide an experimental device for researching the heat transfer influence of roughness on the wall surface of a spray pipe, and provides a method for measuring the wall surface heat transfer process under the conditions of the same fuel gas parameters and different roughness in the spray pipe.
The invention adopts the following technical scheme: an experimental device for researching heat transfer effect of roughness on a spray pipe wall surface comprises:
a nozzle housing having an inlet and an outlet and presenting a cylindrical shape expanding from the inlet to the outlet;
the graphite temperature measuring piece is of a hollow cylinder structure arranged close to the inner wall of the outlet section, the graphite temperature measuring piece is uniformly divided into n graphite temperature measuring units along the outer wall surface of the graphite temperature measuring piece, and the roughness of the surface of each graphite temperature measuring unit, which is in contact with the fuel gas, is different;
the baffle is arranged at the outlet end of the spray pipe shell, is a positioning piece with a fuel gas outflow outlet and is used for positioning the graphite temperature measuring piece;
the thermocouple comprises a plurality of thermocouples, a plurality of thermocouple groups and a plurality of thermocouple groups, wherein the thermocouples are arranged on an outlet section of the spray pipe shell, are specifically distributed on a plurality of sections with different expansion ratios, and are arranged on each section in a surrounding manner and have different arrangement depths;
the thermocouple is used for measuring the change rate of the internal temperature of the wall surface of the outlet section of the spray pipe shell along with the working time of the engine.
Furthermore, the insertion depths of all thermocouples on the same section are different; the depth arrangement rule of each thermocouple on each section is the same.
Furthermore, on each section, the thermocouples are divided into m groups, the insertion depths of the thermocouples in each group are sequentially arranged according to an arithmetic progression, and the thermocouples in each group are arranged according to the same rule.
Furthermore, the graphite temperature measuring pieces are sealed by high-temperature-resistant epoxy resin.
Furthermore, the baffle is an annular positioning piece or n unit positioning pieces with the same shape as the graphite temperature measuring unit, and the unit positioning pieces are combined to form a complete ring.
Furthermore, the graphite temperature measuring piece is high-strength graphite.
Furthermore, the device also comprises a gas generator, a convergence section and an equal straight section which are sequentially connected in series, wherein the outlet of the equal straight section is communicated to the inlet of the spray pipe.
The invention has the beneficial effects that: graphite materials with different roughness are spliced at the position of a simulated solid rocket engine spray pipe to form a spray pipe expansion section, temperature measuring points with different depths are arranged at the cross sections of the graphite with different expansion ratios, thermocouples are arranged at the temperature measuring points, and the temperature change of each temperature measuring point is measured while the engine works. The device can simulate the flow state of the actual nozzle expansion section of the solid rocket engine, and can measure the real-time temperature change of the inner wall surfaces of the nozzles with different roughness in the working state of the engine.
Drawings
FIG. 1 is a schematic view of a nozzle structure of an experimental apparatus for studying the heat transfer effect of roughness on the wall surface of a nozzle tube according to the present invention;
FIG. 2 is a cross-sectional view taken along line A-A of FIG. 1;
FIG. 3 is a cross-sectional view taken along line B-B of FIG. 1;
FIG. 4 is a cross-sectional view taken along line C-C of FIG. 1;
FIG. 5 is a schematic structural diagram of an experimental apparatus for studying the influence of roughness on heat transfer of a nozzle wall surface according to the present invention;
fig. 6 is a diagram showing a simulation calculation result of the heat transfer coefficient between the fuel gas and the wall surface of the experimental device for researching the heat transfer effect of the roughness on the wall surface of the nozzle pipe.
The combustion chamber comprises a front end socket 1, a combustion chamber shell 2, a propellant 3, an ignition explosive bag 4, a sealing plug 5, a pressing cap 6, a convergence section shell 7, an equal straight section shell 8, a spray pipe shell 9, a graphite throat liner 10, a graphite temperature measuring piece 11, a baffle 12 and a thermocouple 13.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention provides an experimental device for researching heat transfer influence of roughness on the wall surface of a spray pipe, which comprises a spray pipe shell 9, a graphite temperature measuring piece 11, a baffle 12 and a plurality of thermocouples 13 as shown in figures 1-4. A plurality of thermocouples 13 are used to measure the rate of change of the internal wall temperature of the outlet section of the nozzle housing 9 with engine on time. The nozzle housing 9 has an inlet and an outlet, and has a cylindrical shape expanding from the inlet to the outlet.
The graphite temperature measuring piece 11 is of a hollow cylinder structure arranged close to the inner wall of the outlet section, the graphite temperature measuring piece 11 is equally divided into n graphite temperature measuring units along the outer wall surface of the graphite temperature measuring piece, and the roughness of the surface of each graphite temperature measuring unit in contact with the fuel gas is different. The cross section of each graphite temperature measuring unit is fan-shaped, and n graphite temperature measuring units with different roughness are combined into a complete graphite temperature measuring part 11, so that the test environment of the inner wall surface with various roughness is provided in one test. The method is mainly used for measuring the heat transfer conditions of the walls with different roughness, and is characterized in that the heat transfer difference generated under different wall conditions is reflected, the number of the temperature measuring units can be selected according to specific experimental requirements, from the machining point of view, the more the temperature measuring units are, the greater the difficulty in machining and subsequent assembly is, and the number of the temperature measuring units is recommended to be reasonably selected according to actual conditions. The roughness is mainly set according to the research purpose, if only the heat transfer difference caused by different roughness is verified, the wall surface roughness of different temperature measuring units can be set to be different arbitrary values, but if the specific influence of different roughness on the heat transfer value needs to be researched, the value of the roughness needs to be strictly represented.
The invention aims to verify the heat transfer difference under different roughness wall surface conditions and research the specific reasons of the heat transfer difference, so that more accurate temperature change needs to be measured.
The baffle plate 12 is arranged at the outlet end of the nozzle shell 9, and is a positioning part with a fuel gas outlet, and is used for positioning the graphite temperature measuring part 11. The main effect of separation blade is for the location, and the temperature measurement subassembly that restricts in the spray pipe produces the displacement under the promotion of high temperature gas, influences the experiment effect. In the aspect of configuration setting, all temperature measuring assemblies are integrally fixed in an annular mode, or a single temperature measuring unit is respectively fixed according to the number of the temperature measuring units, and the fixed range of the blocking piece does not influence the normal outflow of the fuel gas at the outlet of the spray pipe.
A plurality of thermocouples 13 are arranged on the outlet section of the nozzle housing 9, in particular distributed over a plurality of sections of different expansion ratios, and on each section there is a plurality of thermocouples 13 arranged circumferentially with different arrangement depths. In some embodiments, the insertion depth of each thermocouple on the same cross section is different; the depth arrangement rule of each thermocouple on each section is the same. In some embodiments, on each cross section, the thermocouples are divided into m groups, the insertion depths of the thermocouples in each group are sequentially arranged according to an arithmetic progression, and the thermocouples in each group are arranged in the same rule. Such as: the insertion depth of the thermocouples on each section is circularly arranged according to the rule of 2mm, 4mm and 6 mm.
The depth arrangement of the thermocouples on the same section is in accordance with a certain rule, and the depth of the thermocouples on the first section is assumed to be 2mm, 4mm and 6mm respectively, so that the depth of the thermocouples on the subsequent sections is kept consistent, the temperature difference is conveniently compared, and the rule is summarized. The number and specific depth of thermocouple arrangements on each section can be determined according to specific experimental requirements and machining accuracy.
The nozzle extension section of a simulated solid rocket engine is usually made of metal (mostly 30CrMnSiA steel), and the characteristics of high strength and excellent cutting processing of heavy steel are mainly considered. Although steel has certain thermal conductivity, physical parameters of the steel are unstable at high temperature (for example, the thermal conductivity of the steel is greatly changed along with the increase of the temperature), the solid rocket engine has short working time, and a temperature measuring device is difficult to accurately measure the accurate temperature change in the steel shell. Therefore, in the aspect of the material of the spray pipe, a material which has better heat-conducting property than steel, strong thermal stability and easy processing needs to be selected, and high-strength graphite is selected as the material of the inner wall surface of the spray pipe. The graphite heat-conducting property is 2-3 times of that of steel, and meanwhile, the graphite heat-conducting property has stable physicochemical property under the temperature condition of 2500K, and normal cutting processing can be carried out, so that the configuration requirement of the molded surface of the spray pipe is met. The toughness of the graphite material is not enough, and the shell is made of the material outside the device, so that the integral strength of the graphite spray pipe is ensured. In the concatenation in-process, need guarantee the holistic gas tightness of spray tube under high temperature high pressure environment, the spray tube expansion section here contacts with the casing and has adopted the socket joint structure, also can be better when the structure location the leakproofness of ensuring the device, adopts high temperature resistant epoxy to seal between each different roughness wall. Experiments prove that the device can accurately measure the temperature response change of the expansion section of the spray pipe under the conditions of different roughness wall surfaces in the working process of the engine.
Fig. 1 is an assembly schematic diagram of a temperature measuring unit and a spray pipe shell in a spray pipe, wherein a graphite temperature measuring piece and the spray pipe shell are assembled according to the assembly schematic diagram, in order to solve the problem of sealing, high-temperature-resistant epoxy resin is required to be coated on the contact part of the graphite temperature measuring component and the spray pipe shell, and the graphite temperature measuring piece and the spray pipe shell are kept still for more than 24 hours, so that the epoxy resin is ensured to be completely air-dried, and the air tightness of the spray pipe component in the experimental process is ensured. Then, a blocking piece is installed, all parts are assembled according to the general assembly drawing of FIG. 5, the parts are integrally fixed on an engine experiment bench to carry out experiments after the assembly is completed, personnel safety needs to be paid attention to in the experiment process, the working state of each thermocouple along with time in the working process of the engine needs to be measured, a temperature curve is obtained, and the influence of roughness on the wall surface heat transfer of the spray pipe is analyzed according to the temperature change of each measuring point.
As shown in FIG. 5, the experimental device for researching the influence of roughness on the heat transfer of the wall surface of the nozzle tube further comprises a gas generator, a convergence section and an equal straight section which are sequentially connected in series, wherein an outlet of the equal straight section is communicated to an inlet of the nozzle tube. It includes the part is: the device comprises a front seal head 1, a combustion chamber shell 2, a propellant 3, an ignition explosive bag 4, a sealing plug 5, a pressing cap 6, a convergence section shell 7, an equal straight section shell 8, a spray pipe shell 9, a graphite throat liner 10, a graphite temperature measuring piece 11 and a baffle 12.
Examples
The expansion section of the spray pipe is formed by splicing four graphite temperature measuring parts with different surface roughness, and all parts are bonded by high-temperature resistant epoxy resin to achieve the sealing effect. Four graphite temperature measuring pieces with different roughness are annularly and uniformly distributed to form a complete spray pipe expansion section, temperature measuring points with different depths are arranged at different expansion ratio sections along the axial direction of the expansion section, for example, A, B, C three sections are arranged in figure 1, and in the working process of an engine, a thermocouple at the temperature measuring points can measure the change rate of the internal temperature of the wall surface of the spray pipe along with the working time of the engine. After the spray pipe is spliced, the spray pipe is integrally placed in the spray pipe shell, the spray pipe shell is made of steel materials, the overall strength can be guaranteed, meanwhile, the spray pipe shell is compared with graphite, the heat conductivity coefficient of the steel materials is lower, and the influence on an experimental result is smaller. The front end of the graphite spray pipe is provided with a baffle plate, so that the graphite spray pipe is prevented from being blown by fuel gas in the working process to generate slippage.
The working process of the solid rocket engine is roughly as follows: the ignition explosive charge is ignited by the igniter to generate a large amount of heat to ignite the propellant grains, so that high-temperature gas is generated, passes through the convergence section and the equal-straight experimental section, forms supersonic fluid in the expansion section of the spray pipe, and is finally discharged through the outlet of the spray pipe. The experimental engine mainly comprises a fuel gas generator, a convergence section, an equal straight section and a spray pipe, wherein all the parts are connected by flanges, and the flanges are sealed by O-shaped sealing rings, so that the sealing performance of the whole engine shell in the working process of the engine is ensured. And the convergence section is connected with the spray pipe by using an equal straight experimental section shell, and the equal straight experimental section can rectify gas flowing out of the convergence section.
Due to the high-temperature and high-pressure working environment inside the solid rocket engine, the engine simulation experiment cannot easily set too long working time for safety consideration, meanwhile, the response time required by temperature conduction is also considered, and the working time of the engine is recommended to be 5-10 s. Because the working time is short, the high-strength graphite is recommended to be used in the selection of the temperature measuring spray pipe material, and the reasons are as follows: the graphite has good heat-conducting property, good thermal stability in a high-temperature environment, can quickly generate temperature change in the experimental process, is easy for acquisition and subsequent analysis of experimental data, has good cutting processing property, and can be processed into the wall surfaces of the spray pipes with different roughness according to design requirements.
Fig. 6 is a simulation calculation result of the heat transfer coefficient between the gas and the wall surface under the condition of the wall surface with different roughness and a certain gas parameter in the embodiment, it can be seen that the heat transfer is changed due to the difference of the wall surface roughness, and the measurement result of the experimental device provides data support for the study of the heat transfer process under the conditions of the gas in the nozzle and the wall surface with different roughness.
The experimental device is mainly used for researching the influence of the roughness of the inner wall surface of the spray pipe on the flow and heat transfer of the inner wall surface of the spray pipe under the same spray pipe flow condition. Aiming at the problem, the invention mainly adopts the mode of splicing spray pipes with different roughness, and can measure the temperature change at different expansion ratios under the condition of different roughness wall surfaces by replacing the graphite temperature measuring piece at the expansion section. The experimental device can simulate the flow state in the nozzle of a real solid rocket engine. Because its spray tube uses polylith graphite spray tube subassembly to assemble in the hoop, so there are multiple roughness in the spray tube is inside, can survey the influence that wall roughness flows and heat transfer to the gas in the expansion section under certain gas state. Although results can be obtained by performing a plurality of experimental measurements using a single rough wall surface, the following problems occur: the consistency of the multiple experimental gas parameters is difficult to ensure, and the influence of the wall surface roughness on the gas flow and the heat transfer is likely to be caused by the difference of the gas parameters to cause the deviation of the result. According to the design idea of the experimental device for researching the heat transfer effect of the roughness on the wall surface of the spray pipe, the consistency of the gas flow parameters can be ensured, and the heat transfer results of the wall surfaces with different roughness can be measured. Therefore, the invention adopts graphite materials with different roughness to splice and form the nozzle expansion section at the position of the simulated solid rocket engine nozzle, temperature measuring points with different depths are arranged at the sections of the graphite with different expansion ratios, thermocouples are arranged at the temperature measuring points, and the temperature change at each temperature measuring point is measured while the engine works. The device can be used for measuring the real-time temperature change of the inner wall surfaces of the spray pipes with different roughness in the working state of the engine, provides a method for measuring the heat transfer process of the wall surfaces under the conditions of the same fuel gas parameters and different roughness in the spray pipes, and solves the problem of how to measure the heat transfer process of the wall surfaces under the conditions of different roughness in the spray pipes under the same fuel gas parameters.
Claims (6)
1. An experimental device for researching heat transfer influence of roughness on wall surface of spray pipe is characterized by comprising:
a nozzle housing (9) having an inlet and an outlet and presenting a cylindrical shape expanding from the inlet to the outlet;
the graphite temperature measuring component (11) is of a hollow cylinder structure which is arranged close to the inner wall of the outlet section of the spray pipe shell (9), the graphite temperature measuring component (11) is uniformly divided into n graphite temperature measuring units along the outer wall surface of the graphite temperature measuring component, the cross section of each graphite temperature measuring unit is fan-shaped, the graphite temperature measuring units are combined into a complete graphite temperature measuring component, and the roughness of the surface of each graphite temperature measuring unit, which is in contact with the fuel gas, is different;
the baffle plate (12) is arranged at the outlet end of the spray pipe shell (9), is a positioning piece provided with an outlet for gas to flow out and is used for positioning the graphite temperature measuring piece (11);
the thermocouples (13) are arranged on the outlet section of the spray pipe shell (9), the temperature measuring points of the thermocouples are distributed on the sections of the graphite temperature measuring piece (11) with different expansion ratios along the axial direction, and a plurality of thermocouples (13) with different arrangement depths are arranged on each graphite temperature measuring unit of each section in a surrounding manner;
on each graphite temperature measuring unit of each section, thermocouples (13) are in a group, the insertion depth of the thermocouples (13) in each group is sequentially arranged according to an arithmetic progression, and the arrangement rule of the thermocouples (13) in each group is the same;
the thermocouples (13) are used for measuring the change rate of the internal temperature of the wall surface of the outlet section of the spray pipe shell (9) along with the working time of the engine.
2. The experimental device for researching the heat transmission influence of roughness on the wall surface of the spray pipe as claimed in claim 1, wherein the depth arrangement rules of the thermocouples (13) on different sections are the same.
3. The experimental device for studying the heat transmission effect of roughness on the wall surface of the spray pipe as claimed in claim 1, wherein each graphite temperature measuring unit is sealed by high temperature resistant epoxy resin.
4. The experimental device for researching the heat transmission influence of roughness on the wall surface of the spray pipe as claimed in claim 1, wherein the baffle plate (12) is an annular positioning piece or n unit positioning pieces with the same shape as the graphite temperature measuring unit, and the unit positioning pieces are combined to form a complete ring.
5. The experimental device for researching heat transfer influence of roughness on the wall surface of the spray pipe according to claim 1, wherein the graphite temperature measuring piece (11) is high-strength graphite.
6. The experimental device for researching the heat transfer influence of roughness on the wall surface of the nozzle pipe as claimed in claim 1, further comprising a gas generator, a convergent section and an equal straight section which are connected in series in sequence, wherein an outlet of the equal straight section is communicated to an inlet of the nozzle pipe.
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| CN115355112B (en) * | 2022-10-20 | 2023-03-03 | 北京星河动力装备科技有限公司 | Test device for thermal ablation degree of supersonic velocity zone of spray pipe and thermal ablation evaluation method |
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| JP2012242227A (en) * | 2011-05-19 | 2012-12-10 | Hugle International Inc | Temperature detection wafer |
| CN110823400A (en) * | 2019-11-25 | 2020-02-21 | 南京理工大学 | Integral measuring device for temperature and ablation amount of spray pipe and manufacturing method thereof |
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| JP2001085488A (en) * | 1999-09-16 | 2001-03-30 | Bridgestone Corp | Thermometer wafer |
| US6499289B1 (en) * | 2000-03-31 | 2002-12-31 | Alliant Technologies Inc. | Pyrolytic graphite gauge for measuring heat flux |
| CN104061089B (en) * | 2014-05-18 | 2017-01-04 | 西北工业大学 | A kind of solid fuel melting characteristic test device and method of testing |
| CN104833768B (en) * | 2015-03-11 | 2016-08-17 | 西北工业大学 | The analog of rocket engine endoparticle phase sedimentary condition lower thermal insulating layer ablation |
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| JP2012242227A (en) * | 2011-05-19 | 2012-12-10 | Hugle International Inc | Temperature detection wafer |
| CN110823400A (en) * | 2019-11-25 | 2020-02-21 | 南京理工大学 | Integral measuring device for temperature and ablation amount of spray pipe and manufacturing method thereof |
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